Question

The average age of 6 sons of a family is 8 years. The average age of the sons together with their parents is 22 years. If the father is 8 years older than the mother, then the age of the father (in years) is:

• A. 70
• B. 68
• C. 66
• D. 65

Hint:

To solve such questions, first find the total age of the sons and then calculate the total age of the family using the average.

Answer 1

The Correct Option is B

Let the age of the mother be \( x \) years, and the age of the father is \( x + 8 \) years. The total age of the 6 sons is: \[ \text{Total age of sons} = 6 \times 8 = 48 \text{ years}. \] The total age of the family (sons + parents) is: \[ \text{Total age of family} = 48 + x + (x + 8) = 48 + 2x + 8 = 56 + 2x. \] The average age of the family is 22 years, so: \[ \frac{56 + 2x}{8} = 22 \quad \Rightarrow \quad 56 + 2x = 176 \quad \Rightarrow \quad 2x = 120 \quad \Rightarrow \quad x = 60. \] Thus, the age of the father is \( x + 8 = 60 + 8 = 68 \) years, which corresponds to option (2).